Problem: Given $ m \angle MON = 2x + 33$, $ m \angle LOM = 3x + 20$, and $ m \angle LON = 113$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {3x + 20} + {2x + 33} = {113}$ Combine like terms: $ 5x + 53 = 113$ Subtract $53$ from both sides: $ 5x = 60$ Divide both sides by $5$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 2({12}) + 33$ Simplify: $ {m\angle MON = 24 + 33}$ So ${m\angle MON = 57}$.